Closed - Users have more security (ex: recent reports state that Android users are being infected by trojans disguised fake Instagram apps)

link: http://www.theregister.co.uk/2012/04/19/instagram_android_sms_trojan/

BUT developers can spend months building something essentially inside Apple's jail (and then we are still faced with the approval process)

Open - Users can install any application they want, and apps have the ability to access the device's file structure, etc.

- Large amount of non-curated, unfiltered content - Higher potential for social engineering attacks to get bad code on people's devices